A frontal air intake may improve the natural ventilation in urban buses

In this report we analyze the air flow across the open windows (natural ventilation) of an urban bus model and the consequent dispersion of aerosols emitted in the passengers area. The methods include computational fluid dynamics simulations and three ways to characterize the dispersion of passive tracers: a continuous concentration-based model, a discrete random model and a parametric scalar based on the so-called mean age of air. We also conducted experiments using a 1:10 scale bus model and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{CO}_{2}$$\end{document}CO2 as a passive tracer to assess the ventilation characteristics. We found that dispersion and expulsion of aerosols is driven by a negative pressure in the standard bus design equipped with lateral windows. Also, the average age of air is 6 minutes while the air flow promotes aerosol accumulation to the front (driver’s area). To speed up the expulsion of aerosols and reduce their in-cabin accumulation, we propose a bus bodywork prototype having a frontal air intake. All the numerical models and experiments conducted in this work agreed that the expulsion of aerosols in this novel configuration is significantly increased while the average age of air is reduced to 50 seconds. The average air flow also changes with the presence of frontal air intakes and, as a consequence, the expulsion of aerosols is now driven by a frontal velocity field.

Email * : jrvelez@ifisica.uaslp.mx S1. Effect of the inlet velocity Figure S1 shows the dissipation of the normalized in-cabin amount of aerosols for the FW configuration setting different air speeds applied on the inlet boundary "i" (see Fig. 8c). It can be observed that the expulsion rates (slopes of the curves) are similar to the original value found for 50km/h, although the time to start expulsion becomes longer as speed decreases due to the increased travel time it takes for the aerosol cloud to reach the windows. In quantitative terms, the time needed to decrease the original amount of aerosols to 0.1% obeys a power law scale, 301.6( ) −1 ; in the 2D simulations; as an example, for 50km/h, the computed time is 6s, while for 10km/h is 30s. Figure S1. Dissipation of the in-cabin amount of aerosols in the FW configuration. The different speeds are 10, 20, 30, 40 and 50 km/h. Simulations were done in 2D using the SST − model. Figure S2 shows the dissipation of the total in-cabin amount of aerosols for the AW configuration (all windows open). In this mesh size dependency study, we varied the mesh defined at the walls of the bus to increase the spatial resolution of the in-cabin zone; the rest of the mesh far from the bus was unchanged.

S2. Mesh size dependency study and solver configuration
For the coarser mesh we used a size of 0.1W (being W=2.5m the bus width) at the lateral walls of the bus, while at the rear wall we used 51 × 10 −3 W. For the finer mesh we used 6.4 × 10 −3 W at the lateral walls and 3.2 × 10 −3 W at the rear wall. The plot shows that the use of a very coarse mesh renders a dynamic profile clearly different from the rest of the curves (thicker line). In the current simulations we selected a mesh size corresponding to the dashed line (fine mesh). In all the simulations we used a segregated solver, that is, the averaged Navier Stokes equations are solved in a different step from the computation of the turbulent variables within the algorithm loop. On the other hand, for 2D problems, the solver computes the unknown variables vector using matrix factorization (direct solvers such as LU decomposition and its variants). For 3D problems, an iterative solver is chosen so the unknown variables are solved approximately using the Generalized Minimum RESidual method and a preconditioner found by using the algebraic multigrid method (within this last step, the solver finds and initial guess using a coarser mesh and a direct solver). Maximum convergence tolerance was set to 10 −3 .

S3. Simulations without turbulent mixing
In Figure 2 of the main text, we demonstrate that aerosol expulsion rates obtained with both turbulent models, the − and SST − , are very similar. In Figure S3 we show the same simulations but without considering turbulent mixing in the diffusion-convection equation. It is remarkable that now the differences are accentuated; see for example the 2W case where the average flow obtained with − does not even predicts the expulsion of aerosols. This reveals that, although the mean fluid flow obtained with both models are not exactly the same (as shown next in S4), the fluctuating terms considered in the turbulent mixing smooth out such differences.

S4. 2D fluid flow maps and Reynolds number dependency analysis
The − turbulent model is extensively used due to its versatility and adaptability in different geometries; however, it is known that is not optimal for flows close to walls or past obstacles with strong vortex formation, detachment of streamlines or adverse pressure gradients [1,2]. On the other hand, low or mixed Re formulations, like the SST − model, have shown to improve turbulent flow predictions and have been validated against different experimental data such as flows past a cube in channel flows [3], flow around a hydrofoil at standard temperatures [4], flow across a train at different angles of attack [5], ventilation inside a cubical enclosure [6] and flow and deposition of aerosols in lung airways models [7], to mention a few (these papers also highlight similarities between SST − and other formulations such as RNG − ).
On the other hand, in this work we have also seen that either − or SST − yield similar results for the global expulsion rates. There are, however, some important quantitative differences that we now want to remark. To facilitate the analysis and visualization of the flow fields generated by both models, we have computed the so-called Okubo-Weiss parameter, ℚ, in the 2D simulations defined as [8]: where is the local stretching rate: is the local shearing rate: ( ⃗) = ̅ + ̅ and is the local vorticity: ( ⃗) = ̅ − ̅ ℚ is defined in such a way that positive values mean that the local flow is dominated by deformation, while negative values reflect a flow dominated by local rotating elements. Figure S4 shows the ℚ values obtained for the 4W configuration and using both turbulent models. We can see in the corresponding 2D contour plots that both models yield a similar flow field: air enters through the rear windows (denoted with white arrows) forming vortices inside the bus (denoted with asterisks) and leaves the bus through the front windows forming vortices outside the bus: this is the pumping back-to-front effect commented in the main text. On the other hand, we can also observe some quantitative differences between the models; particularly, the − underpredicts the vorticity intensity in some parts inside the bus.
In the main text we also mentioned that we chose the air traveling time, = / , as the scaling parameter for the experimental 1:10 model. However, this scaling option will reduce the Reynolds number by a factor of 100 even though the flow is still turbulent. To see what happens if we change Re by a factor of 100, we computed the 2D flow field for the 4W configuration at = 2 × 10 4 and 2 × 10 6 . The results are plotted in Figure S5 where the blue lines denote the average streamlines, and the color map indicates the value of the turbulent kinetic viscosity [m 2 /s]. Interestingly, notice that the average flow structure is similar in both cases as well as the spatial distribution of ; however, the magnitude of changes by a factor of 100. Figure S4. 2D Okubo-Weiss parameter ℚ computed for the 4W configuration and using both turbulent models. The wind direction (50km/h) is indicated with an arrow. Bus walls are marked with gray lines.

S5. General map of the mean age of air
In Figure 3 of the main text we included the 3D-contours of the mean age of air, , for the 4W and FW cases, specifically for the in-cabin zone. Here we present a general view of the mean age of air appearing in the whole computational domain. In Figure S6 we can see that = 0 at the inlet wall, which is where air   Figure S7 shows the 2D pressure map, together with some streamlines and the velocity field, found in a configuration where we included a driver's window in windward position (marked with asterisks). The backto-front pumping effect at the lateral walls is still observed together with the negative pressure distribution inside the bus. 8 Figure S8 shows a comparison of the CO2 amount measured inside the bus with and without passengers (manikins) for the 4W and FW cases. We can observe that the initial expulsion rate is larger (slopes of the curves) when the passengers are present, in accordance with the reduced age of air values obtained in the simulations including passengers.

S8. Age of air in an occupied bus: high-resolution manikins
In the main text we show that when the bus contains seated passengers, the mean age of air reduces from 50 to 32s in the frontal window configuration, that is, aerosols are expelled more rapidly from the bus when passengers are present. We ran an additional simulation using high-resolution manikins, but unfortunately, we didn't get a converged solution (error below 10 −3 ) after several days of computation (total elements were around 3.5 × 10 6 ). For the unique purpose of sharing these results having an associated error of 8%, we included here the corresponding age of air map; see Figure S9. Although the plot cannot be taken as a definite and rigorous result, the distribution looks similar to the plot included in the main text using lowresolution manikins, giving for this case an average age of air value of 44s and an average internal flow of 0.87m/s (for the empty bus the values were 50s and 0.8m/s, respectively).